The peer appointed to oversee investigations into historic cover-ups of child abuse within public institutions had to apologise after mistakes were made in a similar investigation into the Church of England two years ago.

Theresa May, the Home Secretary, announced on Monday that a new investigation would be launched into the failures of public institutions in protecting children from abuse.

Lady Butler-Sloss, pictured right, the former high-court judge who oversaw the Cleveland inquiry into abuse in the late 1980s, was appointed as head of the new inquiry.

The Church of England, along with the NHS and the BBC, is one of a number of organisations that will come under scrutiny.

In 2011 Butler-Sloss oversaw an investigation into the CofE's failings in dealing with abuse cases in which two CofE ministers in Sussex sexually abused boys.

In 2012, a six-page addendum was printed to accompany the report, acknowledging errors in her corroboration of the facts of the case, the Telegraph revealed yesterday.

Critics have also said it is inappropriate for the peer to lead the investigation given that her late brother, Sir Michael Havers, was attorney general during the 1980s at the time of a notorious paedophile cover-up.

At the time, the attorney general was questioned why a senior diplomat who was found to possess a large quantity of child pornographic material, was only cautioned and not prosecuted.

It is possible that Butler-Sloss would have to investigate this episode within the remit of her inquiry.

Butler-Sloss has said she won't step down over the criticisms, but could her appointment limit the effectiveness of the investigation itself?

Arguably, her strong reputation as a specialist in family law, with a particular commitment to listening to child victims, recommends her for the role.

Add to this her years of experience, both in the judiciary and the House of Lords, and you could say that she sufficiently professional that any scandal associated with her brother ought not to be a consideration.

But her experience also counts against her, and some feel she is too much a part of the establishment to be truly independent in her critique.

Labour MP Simon Danczuk told BBC News: "She's part of the establishment and that raises concerns and the relationship in terms of her brother, I think, is too close for comfort."

At a time of heightened concern about child sex abuse it is even more important that appointments to such positions are seen to be above reproof – both as a commitment to the victims and to regain public trust.

The criticism against her appointment is yet further evidence of the lack of trust in public institutions, and the need for impartial oversight, from which the Church is certainly not exempt.